Updated 4:00 p.m.: Republican Sens. Ted Cruz of Texas and Mike Lee of Utah did not attend Tuesday's party luncheon where a number of ideas to avert default were discussed, according to a senator present at the meeting.

Sen. John McCain, R-Ariz. — who has referred to the tea party conservatives as "wacko birds" and has repeatedly called their plan to link defunding of Obamacare to the government shutdown a "fool's errand" — outed the two no-shows.

Cruz and Lee pose two of the most serious threats (outside of maybe the entire House GOP caucus) to getting a debt limit deal before Treasury's Thursday deadline because they could block any unanimous consent request to cede procedural time. At this point, Senate Majority Leader Harry Reid of Nevada has not yet filed cloture on the framework he discussed with Minority Leader Mitch McConnell of Kentucky and the leaders would need such a time agreement to expedite the procedural process for the bill.

CQ Roll Call asked Lee on Monday whether he would be able to make a decision on whether he would block a consent agreement after attending Tuesday's lunch and hearing McConnell explain the contours of the plan. At the time, Lee said "perhaps."

On Monday night, Cruz gathered with House conservatives at a popular Hill restaurant to strategize their plan going forward. It wasn't immediately clear where he was dining for lunch.

Neither Cruz nor Lee's office responded immediately for comment.

Update 4:00 p.m.

Cruz spokesman Sean Rushton said in an email: "He had a previous commitment that went long. He was planning to go to the caucus meeting but that was canceled last minute and he didn't make lunch. Sen. Cruz has made clear that there is no reason we should default on the debt and he will continue working to seek meaningful relief from Obamacare for all Americans."